The modeling of the statistical distribution of eruptive frequency and volume provides basic information to assess volcanic hazard and to constrain the physics of the eruptive process. We analyze eruption catalogs from volcanoes worldwide in order to find "universal" relationships and peculiarities linked to different eruptive styles. In particular, we test (1) the Poisson process hypothesis in the time domain, looking for significant clustering of events or the presence of almost regular recurrence times, (2) the relationship between the time to the next eruption and the size of the previous event (the "time predictable" model), and (3) the relationship between the size of an event and the previous repose time (the "size predictable" model). The results indicate different behavior for volcanoes with "open" conduit regimes compared to those with "closed" conduit regimes. Open conduit systems follow a time predictable model, with a marked time clustering of events; closed conduit systems have no significant tendency toward a size or a time predictable model, and the eruptions follow mostly a Poisson distribution. These results are used to build general probabilistic models for volcanic hazard assessment of open and closed conduit systems.